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Mirror Image Transition States
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Computational Challenges and Artifacts
The computational identification of MITS is notoriously susceptible to numerical artifacts arising from the flatness of the potential energy surface near the saddle point. One persistent issue is the phenomenon termed "Double Inversion Confounding (DIC)/)". DIC occurs when a numerical optimization routine converges to a saddle point that is geometrically near a MITS but lacks the requisite reflection plane… -
Numerical Methods In Chemistry
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The fundamental starting point for many electronic structure methods is the Hartree-Fock approximation , which treats electron-electron repulsion mean-field style. The HF method ultimately reduces to solving the matrix form of the Roothaan-Hall equations :
$$ \mathbf{F} \mathbf{C} \mathbf{S} = \mathbf{S} \mathbf{C} \mathbf{\epsilon} $$
where $\mathbf{F}$ is the Fock matrix , $\mathbf{C}$ contains the [molecular orbital (MO) coefficients](/entries/molecular-orb… -
Numerical Methods In Chemistry
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where $\mathbf{F}$ is the Fock matrix , $\mathbf{C}$ contains the molecular orbital (MO) coefficients , $\mathbf{S}$ is the overlap matrix of the chosen basis set , and $\mathbf{\epsilon}$ holds the orbital energies.
The choice of basis set (e.g., STO-nG, Pople series , Correlation Consistent basis sets ) is critical. Numerical stability often degrades sharply when [basis set… -
Point Group
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The most powerful application of point group theory is through the use of Character Tables. A character table tabulates the irreducible representations (irreps) of the group, which are the fundamental building blocks from which all symmetry behavior is constructed.
Each row in the character table corresponds to one irrep, and the entries in the columns are the characters ($\chi$) of the symmetry operations when acting upon a basis set (e.g., atomic orbitals or [vibrational modes](/entries/vibration… -
Quantum Chemistry
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Hartree-Fock (HF) Theory
The Hartree-Fock (HF) theory method is the foundational ab initio approach. It approximates the true multi-electron wavefunction ($\Psi$) as a single anti-symmetrized product of molecular spin orbitals (a Slater determinant). Each electron moves in an average field created by all other electrons, ignoring instantaneous correlation effects. The orbitals are determine…